ABSTRACT Adaptation of the attractant response in Escherichia coli is attributable to the methylation of its transmembrane chemotactic receptors by the methyltransferase CheR. This protein contains two binding domains, one for the sites of methylation themselves and the other for a flexible tether at the C terminus of the receptor. We have explored the theoretical consequences of this binding geometry for a CheR molecule associated with a cluster of chemotactic receptors. Calculations show that the CheR molecule will bind with high net affinity to the receptor lattice, having a high probability of being attached by one or both of its domains at any instant of time. Because of the relatively low affinity of its individual domains and the close proximity of neighboring receptors, it is likely that when one domain unbinds it will reattach to the array before the other domain unbinds. Stochastic simulations show that the enzyme will move through the receptor cluster in a hand-over-hand fashion, like a gibbon swinging through the branches of a tree. We explore the possible consequences of this motion, which we term "molecular brachiation", for chemotactic adaptation and suggest that a similar mechanism may be operative in other large assemblies of protein molecules.
INTRODUCTION
The coliform bacterium Escherichia coli detects attractants and repellents in its environment by means of four homologous, dimeric receptors, Tar, Tsr, Trg, and Tap (Mowbray and Sandgren, 1998). These receptors are composed of an N-terminal periplasmic domain, a transmembrane region, and a long (~26 nm), coiled-coil cytoplasmic domain (Bass et al., 1999; Kim et al., 1999). The receptors tend to aggregate at the poles of the cell in a relatively stable complex with two other proteins of the chemotaxis signaling pathway, the histidine kinase, CheA, and the linking protein, CheW (Maddock and Shapiro, 1993). CheA autophosphorylates at a rate controlled by the ligand occupancy of the receptors, and acts as a phosphodonor for the response regulator, CheY. Phosphorylated CheY (CheYp) diffuses through the cytoplasm and binds to the switch complex at the base of the flagellar motor, thereby modifying the swimming behavior of the bacterium (Falke et al., 1997; Armitage, 1999; Bren and Eisenbach, 2000).
The receptors have four or five sites (glutamate or deamidated glutamine residues) in their cytoplasmic domains that undergo reversible methylation catalyzed by the methyltransferase, CheR, and the methylesterase, CheB (Mowbray and Sandgren, 1998; Zhulin, 2001). Together, these enzymes mediate adaptation of the chemotactic response by modifying the methylation state of the receptors to restore the activity of CheA (altered by the binding of ligands to the periplasmic domain of the receptors). In addition to interacting with the methylation sites midway along the cytoplasmic domain of the receptors, both CheR and CheB also interact with a second site at the extreme C terminus of the cytoplasmic domain (Wu et al., 1996). A crystallographic study has shown that the C-terminal pentapeptide of the major receptors, Tar and Tsr, binds to CheR in a sub-- domain remote from the active site (Djordjevic and Stock, 1998). Biochemical studies have shown that the presence of the pentapeptide is required for both CheR and CheB to work efficiently (Okumura et al., 1998; Barnakov et al., 1999; Shiomi et al., 2000). The pentapeptide is separated from C terminus of the cytoplasmic coiled-coil by a flexible tether (Le Moual and Koshland, 1996), which should enable either enzyme not only to modify sites on the receptor to which it is bound, but also on its immediate neighbors in a cluster of receptors. Direct experimental evidence for an interdimer mechanism of this kind has been obtained in the case of CheR, but not for CheB (Le Moual et al., 1997; Li et al., 1997).
In this study, we consider how the activity of CheR in particular (and by extension CheB) might be affected by its ability to bind to receptors at two distinct sites and by the tendency of chemotactic receptors to form large, lateral aggregates in the plasma membrane. The paper is divided into the following sections.
In the first section entitled Generic Model of a Brachiating Protein, we consider a generic model that illustrates a number of important features of the binding and diffusive movement of a bivalent "dumbbell" molecule, with two binding domains connected by a flexible linker, over a lattice of binding sites. We show that this dumbbell molecule will bind tightly to the lattice and yet undergo restricted diffusive motion within the cluster, moving by a novel hand-over-hand mechanism we term "molecular brachiation."
In the second section, Specific (CheR) Model, we provide a more specific model of the interaction of CheR molecules with the receptor lattice and show that, despite many differences, it nevertheless retains the essential features of a brachiating molecule, as seen in the case of the dumbbell protein. The many combinatorial possibilities arising in this situation are explored using a program that handles the interactions between individual molecules in a stochastic manner, from which we derive quantitative estimates of the movements of CheR molecules within the receptor lattice.
In the third section entitled Implications for Chemotaxis, we examine the implications of our analysis for the process of chemotactic adaptation and address the possibility of a variable binding affinity of CheR to the receptors and other complications in a nonquantitative manner. Finally, in section 4, Molecular Brachiation, we explore the more general implications of molecular brachiation for large arrays of protein molecules in other cells.
GENERIC MODEL OF A BRACHIATING PROTEIN
Consider a hypothetical model in which a dumbbell-shaped molecule with two identical binding domains linked by a short, flexible tether, freely diffusing in aqueous solution, encounters a regular lattice of sites to which it can bind (Fig. 1). Initial contact will be through a conventional bimolecular binding and occur at a rate proportional to the concentration of freely diffusing molecules. However, once the first domain has attached to the lattice, then the effective concentration for binding of the second domain will depend only on the length and physical properties of the tether and on the positions of nearby lattice sites. Under suitable conditions, the "effective concentration" of this second domain may be very much higher than the concentration of freely diffusing molecules, and this will enhance the probability of the molecule existing in the doubly bound form.
How tight will the binding of the dumbbell molecule be? If we assume for simplicity that the two domains have identical (diffusion-limited) association rates, kon, and dissociation rates, koff, then, for the binding of unattached dumbbell molecules, concentration R, to a lattice of binding sites, concentration T, we have the following equilibrium conditions:
IMPLICATIONS FOR CHEMOTAXIS
There is no direct evidence for the movement of CheR by brachiation through clusters of chemotactic receptors. The most unequivocal proof would require the visualization of individual CheR molecules in a cluster and observation of their residency and diffusive motion. This would certainly be difficult, not only because of the minute size of the clusters but also their inaccessibility. One could hope to produce larger clusters in cells, perhaps on those generated by inhibitors of septation (Maki et al., 2000), or even to reconstruct large clusters in vitro by the self-assembly of proteins in an artificial membrane. Membrane fractions from bacteria are indeed routinely used in the analysis of chemotaxis function, but the chemotactic receptors comprise a small fraction of the total membrane protein and the extent of clustering in the absence of cytoplasmic components remains uncertain.
There is, however, indirect or circumstantial evidence that all the conditions are in place in the living cell for brachiation of CheR to occur. To recapitulate, CheR has two distinct binding sites for the receptor: one that binds the C terminus and one that recognizes the glutamate residues that undergo methylation. Moreover, the C-terminal pentapeptide involved in binding is situated at the end of a sequence of amino acids (estimated to be ~30 residues long) that appears to have no regular structure. In such a situation, provided that the arrangement of receptor dimers in the cluster is reasonably regular and the separation between adjacent receptors is not too great, a CheR molecule attached to this site should be capable of reaching a neighboring receptor in the cluster and binding to it with enhanced affinity. Consistent with this view, there is direct biochemical evidence that CheR can catalyze the modification of one receptor while being anchored to a neighboring receptor through the flexible tether (Le Moual et al., 1997; Li et al., 1997). Moreover, it has been shown that deletion of part or all of the tether, which should abolish brachiation, reduces the activity of CheR by between one and two orders of magnitude (Le Moual et al., 1997; Li et al., 1997; Bamakov et al., 1999). If detachment and re-attachment of a CheR molecule occur at its two sites independently but at similar rates, there will be an opportunity, during episodes in which it is attached at just one site, for diffusive movement to occur. In other words, the CheR molecule could move from receptor to receptor in a manner reminiscent of a gibbon swinging through the branches of a tree, hence the term molecular brachiation.
What will be the consequences of this novel motion for chemotaxis? One salient feature of the proposed diffusive motion is that the time spent by a CheR molecule in contact with an individual receptor will be relatively brief. If the two binding sites have identical values of K^sub d^ of 2 (mu)M, then the time spent in association with either site would average 0.1 s. Interestingly, this duration matches quite well the time taken to add a methyl group to a receptor, as purified CheR in vitro has a V^sub max^ of ~10 methyl groups per receptor per minute (Simms et al., 1987) (and estimates based on the in vivo rate of adaptation give a similar value). In broad terms, therefore, the mechanism of brachiation should allow a CheR molecule time to methylate each receptor to which it binds before moving on to a different one. A simple binding interaction through a high-affinity site, by contrast, would be expected to produce a much longer dwell time. With a single binding site with a K^sub d^ of 4 nM, an enzyme would remain attached to an individual receptor for 50 s or so, which is incompatible with the observed catalytic rate.
Much of what has been said so far regarding CheR could also be applied to the demethylating enzyme CheB. This similarly sized enzyme also has two binding sites, one for a methylated residue on a receptor and the other for the C-terminal flexible tether. Although details of the interaction differ (Barnakov et al., 2001), it seems likely that CheB could also work in both an intra- and an interdimer manner, allowing it to brachiate through the receptor cluster. Another difference relates to the number of CheB molecules in the cell, apparently some 10 times higher than that of CheR (Simms et al., 1985). However, given that CheB is activated by autophosphorylation (using phosphorylated CheA as a phosphodonor), it may be that the number of active CheB molecules in a cell is not very different from the number of CheR.
There is no doubt that the actual situation in a real cluster of receptors is much more complicated than that portrayed here. Not only are there two flexible tethers and eight or 10 methylation sites per receptor dimer, but the clusters themselves are likely to be irregular in size and shape and to include receptors of different types, Tar, Tsr, Trg, and Tap, mixed together. Furthermore, as the low-abundance receptors Trg and Tap lack the C-terminal flexible tethers present on Tar and Tsr, they would be unable to mediate movement by brachiation. In fact, it has been suggested that the efficient methylation and demethylation of the low-abundance receptors will rely on their close proximity to the more abundant Tar and Tsr (Feng et al., 1997; Weerasuriya et al., 1998; Feng et al., 1999). Evidently, the presence of low-- abundance receptors in the lattice will modify, and perhaps disrupt, the smooth progression of a brachiating molecule across the lattice.
An even more fundamental complication is introduced by the conformational changes undergone by receptors in response to ligand binding, which are thought to be the basis of signal transduction in this system (Falke and Hazelbauer, 2001). It is widely believed that CheR methylates only receptors in the conformation that inactivate CheA (a situation favored by attractant binding) (Terwilliger et al., 1986; Shapiro et al., 1995), whereas CheB demethylates only receptors in the conformation that activate CheA (a situation favored by repellent binding) (Borczuk et al., 1986; Sanders and Koshland, 1988). If this scenario is correct, then 1 of the 2 binding domains of CheR (the one associated with the catalytic site) is likely to show a variable K^sub d^ for receptors depending upon their current conformational state and (perhaps) degree of methylation. If, moreover, the binding of CheR or CheB to a receptor actually stabilizes a particular conformation, then these two enzymes will tend to exclude one another and perhaps form local domains of different methylation state within the field of receptors.
In this study, we have assumed for simplicity that the affinity of CheR for the methylation site is the same as for the flexible tether, although physiologically they are likely to differ. If the affinity for the methylation site is weaker, for example, then the higher the value of this Kd, the lower the overall affinity of a CheR molecule for the receptor lattice will be and the more limited in extent its brachiation. Under such conditions, the molecule would be expected to remain attached to an individual tether as it diffuses between the methylation sites in its vicinity. Movement to a new tether would be possible but infrequent, because of the lower affinity of the second site. In a preliminary investigation of this situation, we performed simulations in which values of Kd of the methylation binding site were 100- and 1000-fold higher (that is, 0.2 and 2 mM, respectively), large enough for any differences in behavior to become apparent (Fig. 6). As expected, a CheR molecule in these circumstances becomes more restricted in its ability to diffuse over extended regions within the cluster.
MOLECULAR BRACHIATION
Although we are not aware that the concept of molecular brachiation has been described previously, phenomena of a similar kind have been extensively documented. The existence of "interdomain linkers", or flexible tethers, in bacterial two-- component regulatory systems was noted over a decade ago (Wootton and Drummond, 1989), and a number of examples are known in which their use results in enhancements in local concentration. A particularly well characterized system is the Shaker K+ channel, which has been subject to both experimental and theoretical investigation (Hoshi et al., 1990; Timpe and Peller, 1995). Inactivation of the channel occurs when an N-terminal regulatory domain, attached to the core of the protein by a linker assumed to be free of regular secondary-- structure elements, physically blocks the opening of the pore. Flexible looping is also a feature of protein-DNA interactions, where it serves to bring proteins attached at distant sites, such as those involved in transcriptional regulation, close together (Droge and MOller-Hill, 2001). In eukaryotes, the movement of bivalent molecules along cytoskeletal filaments enables organelles and vesicles to be transported from one location in the cell to another. The agents in this case are two-headed motor proteins such as kinesin or myosin IV, which couple the hydrolysis of ATP to unidirectional motion along the filament. However, it is likely that such molecules would, in the absence of ATP hydrolysis, undergo diffusive random walks or "1-D brachiation" (Vilfan et al., 2001). Moving to three dimensions, we might mention the fact that networks of actin filaments in the membrane cortex of many eukaryotic cells typically contain a variety of bivalent actin-binding proteins. Some of these, such as a-actinin and filamin, have two identical actin-binding domains linked by a flexible tether and so should be able to brachiate within the actin meshwork.
In summary, we suggest that the mechanism of molecular brachiation introduced here could operate in a variety of situations within the cell. It carries the potential advantage of allowing an enzyme or other active molecule to be sequestered to a large structure, without the concomitant requirement that the molecule also becomes effectively immobilized because of high-affinity binding. As shown in this study, a brachiating molecule can move in a diffusive fashion over the surface of a 2-D lattice and thereby spread its activity over the entire structure in a relatively short period of time. This physically realistic property should provide cells with the ability to control self-assembly processes in a sensitive and highly flexible manner.
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[Author Affiliation]
Matthew D. Levin, Thomas S. Shimizu, and Dennis Bray
Department of Zoology, University of Cambridge, Cambridge CB2 3EJ, United Kingdom
[Author Affiliation]
Submitted October 22, 2001, and accepted for publication December 28, 2001.
Address reprint requests to Matthew D. Levin, Department of Zoology, University of Cambridge, Downing Street, Cambridge CB2 3EJ, UK. Tel.: 44-1223-336623; Fax: 44-1223-336676; E-mail: md122@cus.cam.ac.uk.
